US10158363B1 - Josephson and/or gate - Google Patents

Josephson and/or gate Download PDF

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US10158363B1
US10158363B1 US15/811,000 US201715811000A US10158363B1 US 10158363 B1 US10158363 B1 US 10158363B1 US 201715811000 A US201715811000 A US 201715811000A US 10158363 B1 US10158363 B1 US 10158363B1
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logical
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bias
storage
quantizing
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Alexander Louis Braun
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Northrop Grumman Systems Corp
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Priority to US15/811,000 priority Critical patent/US10158363B1/en
Priority to CA3077219A priority patent/CA3077219C/fr
Priority to PCT/US2018/056316 priority patent/WO2019094162A1/fr
Priority to JP2020517893A priority patent/JP6894048B2/ja
Priority to KR1020207012934A priority patent/KR102291321B1/ko
Priority to EP18799635.0A priority patent/EP3711165B1/fr
Priority to AU2018364957A priority patent/AU2018364957B2/en
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03K—PULSE TECHNIQUE
    • H03K19/00—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits
    • H03K19/02—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components
    • H03K19/195—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using superconductive devices
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03K—PULSE TECHNIQUE
    • H03K19/00—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits
    • H03K19/02—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components
    • H03K19/195—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using superconductive devices
    • H03K19/1954—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using superconductive devices with injection of the control current
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03K—PULSE TECHNIQUE
    • H03K19/00—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits
    • H03K19/20—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits characterised by logic function, e.g. AND, OR, NOR, NOT circuits

Definitions

  • the present invention relates generally to quantum and classical digital superconducting circuits, and specifically to a Josephson AND/OR gate.
  • CMOS complimentary metal-oxide semiconductor
  • JJs superconducting Josephson junctions
  • An AND/OR gate is a logical gate having at least two logical inputs and at least two logical outputs, one of the logical outputs representing the AND logical function and another of the outputs representing the OR logical function.
  • the AND output of the AND/OR gate returns an asserted output signal if and only if all of the logical inputs are asserted.
  • the OR output returns an asserted output signal if any one of the logical inputs is asserted.
  • a first logical input is configured to provide a first input single flux quantum (SFQ) pulse to first and second quantizing storage loops.
  • a second logical input is configured to provide a second input SFQ pulse to third and fourth quantizing storage loops.
  • a DC bias input is configured to provide an initializing SFQ pulse to a fifth quantizing storage loop.
  • a first logical decision Josephson junction (JJ) common to the first, fourth, and fifth quantizing storage loops is configured to assert a first logical output based on the first and second logical inputs both being asserted and to de-assert the first logical output based on either or both of the first or second logical inputs being de-asserted.
  • a second logical decision JJ common to the second, third, and fifth quantizing storage loops is configured to assert a second logical output based on either or both of the first or second logical inputs being asserted and to de-assert the second logical output based on the first and second logical inputs both being de-asserted.
  • Another example provides a method of determining logical AND and OR values based on SFQ pulse inputs.
  • An initializing current is established in a bias storage loop comprising first and second logical decision JJs in a reciprocal quantum logic (RQL) AND/OR gate.
  • Positive SFQ pulses are provided to assert one or both logical inputs of the RQL AND/OR gate, thereby placing currents in quantizing logical input storage loops in the RQL AND/OR gate and causing one or both logical decision JJs to be triggered.
  • a logical OR assertion signal propagates from an OR output of the RQL AND/OR gate based on one or both logical inputs being asserted.
  • a logical AND assertion signal can also propagate from an AND output of the RQL AND/OR gate based on both logical inputs being asserted.
  • a superconducting gate circuit which includes a first input configured to provide a first input pulse and a second input configured to provide a second input pulse.
  • the circuit further includes a first storage loop comprising a first quantizing storage inductor interconnecting a first input JJ and a first logical decision JJ, a second storage loop comprising a second quantizing storage inductor interconnecting the first input JJ and a second logical decision JJ, a third storage loop comprising a third quantizing storage inductor interconnecting a second input JJ and the second logical decision JJ, a fourth storage loop comprising a fourth quantizing storage inductor interconnecting the second input JJ and the first logical decision JJ, and a bias storage loop comprising the first and second logical decision JJs.
  • a logical AND output in the circuit is configured to be asserted based on positive input pulses being provided to both the first and second logical inputs.
  • a logical OR output in the circuit is configured to be asserted based on a positive input pulse being provided to at least one of the first and second logical inputs.
  • FIG. 1 is a block diagram of an example Josephson AND/OR gate.
  • FIGS. 2A-2C are circuit diagrams of example Josephson AND/OR gates.
  • FIG. 3A-3J are annotated circuit diagrams of the example Josephson AND/OR gate of FIG. 2A illustrating its functioning.
  • FIG. 4 is a flow chart of an example method of determining logical AND and OR values based on SFQ pulse inputs.
  • a two-input, two-output superconducting gate can be configured to provide two logic functions, such as two different logic functions, in response to a pair of inputs.
  • the two logic functions can correspond to a logic-AND operation and a logic-OR operation on the respective pair of inputs.
  • the inputs can each be provided via a Josephson transmission line (JTL), such as in a reciprocal quantum logic (RQL) superconducting circuit.
  • JTL Josephson transmission line
  • RQL reciprocal quantum logic
  • FIG. 1 shows an example Josephson AND/OR gate 100 having two logical inputs A and B, and two logical outputs AO and OO, corresponding to a logical AND determination and a logical OR determination, respectively.
  • Gate 100 includes output stage 102 , configured to provide outputs AO and OO, and input stage 104 , configured to receive inputs A and B, which can consist of positive or negative single flux quantum (SFQ) pulses corresponding to asserted or de-asserted logic states, respectively.
  • SFQ single flux quantum
  • Logical input A is associated with (e.g., provided to) first storage loop 106 - 1 and second storage loop 106 - 2
  • logical input B is associated with (e.g., provided to) third storage loop 106 - 3 and fourth storage loop 106 - 4
  • a bias storage loop 106 - 5 receives a DC bias input which initializes bias storage loop 106 - 5 at system start-up.
  • Storage loops 106 - 1 , 106 - 2 , 106 - 3 , 106 - 4 , 106 - 5 can be quantizing storage loops, by which it is meant that storage elements therein are sized large enough such that stored current alone, even with the AC bias, is insufficient trigger Josephson junctions at either end, such as JJs 108 - 1 and 108 - 2 .
  • the quantizing nature of the storage loops permits them to stably store a full ⁇ 0 of current for an arbitrary amount of time until some condition is met.
  • First logical decision Josephson junction (JJ) 108 - 1 is common to (i.e., shared by) first and fourth logical input storage loops 106 - 1 , 106 - 4 , as well as bias storage loop 106 - 5 .
  • First logical decision JJ 108 - 1 triggers based on logical inputs A and B both being asserted. The assertion or de-assertion of output AO is based on the triggering of first logical decision JJ 108 - 1 .
  • output AO can propagate a positive SFQ pulse corresponding to an asserted output logic state when both A and B are asserted, and a negative SFQ pulse corresponding to a de-asserted output logic state when either or both of A or B are de-asserted.
  • Second logical decision JJ 108 - 2 is common to (i.e., shared by) second and third logical input storage loops 106 - 2 , 106 - 3 , as well as bias storage loop 106 - 5 .
  • Second logical decision JJ 108 - 2 triggers based on either or both of logical inputs A or B being asserted. The assertion or de-assertion of output OO is based on the triggering of second logical decision JJ 108 - 2 .
  • output OO can propagate a positive SFQ pulse corresponding to an asserted output logic state when either or both of A or B are asserted, and a negative SFQ pulse corresponding to a de-asserted output logic state when both A and B are de-asserted.
  • Bias storage loop 106 - 5 includes both first logical decision JJ 108 - 1 and second logical decision JJ 108 - 2 .
  • Output stage 102 includes two output Josephson transmission lines (JTLs) 110 , 114 to amplify the outputs of logical decision JJs 108 - 1 , 108 - 2 .
  • AND output JTL 110 corresponds to AND output AO
  • OR output JTL 114 corresponds to OR output OO.
  • the triggering of logical decision JJs 108 - 1 , 108 - 2 can be based not only on inputs A and B, but also on bias signals 112 , 116 provided to output stage 102 , e.g., to output JTLs 110 , 114 , respectively.
  • Bias signals 112 , 116 can provide both AC and DC bias.
  • bias signals 112 , 116 can act as a clock to AND/OR gate 100 , causing the evaluation of the inputs A and B to produce the outputs AO, OO at certain points in time according to the AC component of bias signals 112 , 116 .
  • FIG. 2A shows an example Josephson AND/OR gate 200 having two logical inputs ai and bi, a logical AND output ao, and a logical OR output oo.
  • Circuit 200 encodes logical states as JJ superconducting phase, e.g., a zero phase can represent a de-asserted state (“logic 0” or “logic low”) and a 2 ⁇ phase can represent an asserted state (“logic 1” or “logic high”).
  • Inputs ai and bi are coupled to relatively small input inductors FL 6 a _ 0 and FL 6 b _ 0 , respectively.
  • the circuit 200 comprises five storage loops together comprising five storage inductors and four JJs.
  • These storage loops can correspond to loops 106 - 1 through 106 - 5 in FIG. 1 .
  • Four of the storage loops i.e., the input storage loops, each comprise one input JJ, one storage inductor, and one logical decision JJ. Accordingly, each of the four JJs is part of two different input storage loops. Two of these JJs, which are herein termed logical decision JJs, are also part of the fifth storage loop.
  • the circuit also includes two output Josephson transmission lines (JTLs), one associated with each of its logical outputs, which receive AC bias signals (e.g., sinusoidal signals) on respective bias lines bias_ 1 and bias_ 0 .
  • JTLs output Josephson transmission lines
  • the storage inductors Lstoraa, Lstorba, Lstorao, Lstorbo, and Lstorbias can be quantizing storage inductors, by which it is meant that they are sized large enough such that stored current alone, even with the AC bias, is insufficient trigger Josephson junctions at either end, e.g., b 2 a _ 0 , b 2 b _ 0 , b 0 _ 1 , b 0 _ 0 as they pertain in pairs to any corresponding loop.
  • the quantizing nature of the storage loops permits them to stably store a full ⁇ 0 of current for an arbitrary amount of time until some condition is met.
  • a first storage loop comprises first input JJ b 2 a _ 0 , first storage inductor Lstoraa, and first logical decision JJ b 0 _ 1 .
  • a second storage loop comprises first input JJ b 2 a _ 0 , second storage inductor Lstorao, and second logical decision JJ b 0 _ 0 .
  • a third storage loop comprises second input JJ b 2 b _ 0 , third storage inductor Lstorbo, and second logical decision JJ b 0 _ 0 .
  • a fourth storage loop comprises second input JJ b 2 b _ 0 , fourth storage inductor Lstorba, and first logical decision JJ b 0 _ 1 .
  • a first output JTL associated with the logical AND output, consists of first logical decision JJ b 0 _ 1 , inductors FL 4 _ 1 , L 2 _ 1 , and FL 5 _ 1 , and first output JJ b 1 _ 1 .
  • a second output JTL associated with the logical OR output, consists of second logical decision JJ b 0 _ 0 , inductors FL 4 _ 0 , L 2 _ 0 , and FL 5 _ 0 , and second output JJ b 1 _ 0 .
  • bias inductor Lstorbias is connected between the two logical decision JJs, b 0 _ 0 and b 0 _ 1 , to establish the fifth storage loop, a bias storage loop, that is initialized to a certain state at system start-up.
  • Bias inductor Lstorbias can be slightly smaller than inductors that in a different topology (not shown) might be placed between the upper connections of logical decision JJs b 0 _ 1 , b 0 _ 0 and a low-voltage node (e.g., a ground node), yielding an overall more efficient gate.
  • bias inductor Lstorbias can be initialized with application of one ⁇ 0 of current 202 .
  • Such application can be achieved either directly, via a transformer coupling to a DC current 204 , as shown in FIG. 2B , or indirectly, via transformer and quantizing JJ 206 , as shown in FIG. 2C , or by any other suitable mechanism.
  • bias inductor Lstorbias is split into two inductors, bias inductors Lstorbias 1 and Lstorbias 2 , in series with and separated by quantizing JJ bquant, which is connected in parallel with a transformer coupling to a DC bias so as to provide the aforementioned initializing current.
  • This current 202 is shown in FIG. 2A as flowing from the AND side of the gate, b 0 _ 1 , towards the OR side of the gate, b 0 _ 0 .
  • input inductors FL 6 a _ 0 and FL 6 b _ 0 can be sized to provide about 8.5 picohenries (pH) of inductance
  • Storage inductors Lstoraa, Lstorba, Lstorao, Lstorbo, and Lstorbias can all be sized, for example, to provide about 35 pH of inductance.
  • Output JTL inductors FL 4 _ 1 and FL 5 _ 1 can be sized such that their inductances sum to about 14 pH, for example.
  • output JTL inductors FL 4 _ 0 and FL 5 _ 0 can be sized such that their inductances sum to about 14 pH.
  • Bias input inductors L 2 _ 1 and L 2 _ 0 in the output JTLs can be sized to provide appropriate bias current.
  • the given example component sizings can be scaled proportionately.
  • the AC components of bias signals bias_ 1 and bias_ 0 can be the same or about the same phase. By “about,” it is meant within tolerances acceptable for circuit functioning as described herein, e.g., ⁇ 10%.
  • FIGS. 3A through 3J illustrate an example sequence of currents in circuit 200 producing logical outputs consistent with the desired AND/OR functionality.
  • FIG. 3A shows a positive single flux quantum (SFQ) input being applied to second logical input bi, creating current 302 through second input inductor FL 6 b _ 0 and second input JJ b 2 b _ 0 .
  • SFQ single flux quantum
  • FIG. 3B the superconducting phase of second input JJ b 2 b _ 0 is raised from zero to 2 ⁇ , as indicated by the dot over JJ b 2 b _ 0 in FIG. 3B .
  • Second input JJ b 2 b _ 0 is thereby caused to trigger, which has several effects.
  • the triggering annihilates the original input current 302 (not shown in FIG. 3B ) by producing an equal and opposite current.
  • the triggering also puts one SFQ of current 304 into the loop formed by second input JJ b 2 b _ 0 , third storage inductor Lstorbo, and second logical decision JJ b 0 _ 0 , as well as puts one SFQ of current 306 into the loop formed by second input JJ b 2 b _ 0 , fourth storage inductor Lstorba, and first logical decision JJ b 0 _ 1 .
  • Positive bias is thereby applied to both logical decision JJs b 0 _ 0 and b 0 _ 1 .
  • second logical decision JJ b 0 _ 0 now receives two or about two ⁇ 0 of positive current
  • first logical decision JJ b 0 _ 1 now receives zero or about zero ⁇ 0 of positive current, as the two currents 202 and 306 are opposite and equal or about equal.
  • the above sequence illustrates the result of providing an assertion SFQ pulse 302 on second logical input bi alone: an assertion SFQ pulse 310 on output oo alone.
  • an assertion SFQ pulse on first logical input ai alone will not generate an assertion SFQ pulse on output ao alone despite the apparent topological symmetry of circuit 200 with respect to its upper and lower halves.
  • Directional initializing bias current 202 engenders a functional asymmetry that realizes the correct logical functioning of OR and AND outputs oo and ao, respectively.
  • Logical decision JJs b 0 _ 1 and b 0 _ 0 each effectively operate as a 2-of-3 majority gate with respect to currents in the three storage loops connected to each of them—b 0 _ 1 being connected to storage inductors Lstoraa, Lstroba, and Lstorbias, and b 0 _ 0 being connected to storage inductors Lstorbo, Lstorao, and Lstorbias.
  • bias current 202 After initialization of bias current 202 , second logical decision JJ b 0 _ 0 , corresponding to the OR output, sees bias current 202 as a positive current on one of its three storage-loop inputs, while first logical decision JJ b 0 _ 1 , corresponding to the AND output, sees bias current 202 as a negative current on one of its three storage-loop inputs.
  • first logical decision JJ b 0 _ 1 corresponding to the AND output
  • FIG. 3E shows the application of a second positive SFQ input pulse via the first logical input ai to establish current 314 .
  • This triggers first input JJ b 2 a _ 0 , as shown in FIG. 3F , which removes the ⁇ 0 of current 312 from the second storage loop containing second storage inductor Lstorao and places an SFQ 316 into the first storage loop comprising first input JJ b 2 a _ 0 , first storage inductor Lstoraa, and first logical decision JJ b 0 _ 1 , flowing from first input JJ b 2 a _ 0 to first logical decision JJ b 0 _ 1 .
  • first logical decision JJ b 0 _ 1 receives two ⁇ 0 of positive current and triggers, as shown in FIG. 3G , driving an SFQ 318 towards first output JJ b 1 _ 1 , which will then trigger to assert the logical AND output ao by propagating a pulse out that output (not shown). Additionally, it will also destroy current 306 (first generated in FIG.
  • FIG. 3H shows the state of the circuit after first input JJ b 2 a _ 0 has been untriggered to take it from a 2 ⁇ superconducting phase to a zero superconducting phase following the application of a negative SFQ pulse to first logical input ai.
  • a negative current 322 is established in the first storage loop between input JJ b 2 a _ 0 , first storage inductor Lstoraa, and first logical decision JJ b 0 _ 1 .
  • Another negative current 324 is likewise established in the second storage loop between input JJ b 2 a _ 0 , second storage inductor Lstorao, and second logical decision JJ b 0 _ 0 .
  • This untriggering drives a negative SFQ pulse towards second output JJ b 1 _ 0 , which itself untriggers, propagating a negative output pulse out of logical OR output oo to deassert that output. Additionally, this will put one ⁇ 0 of current into the loop including bias inductor Lstorbias flowing from first logical decision JJ b 0 _ 1 to second logical decision JJ b 0 _ 0 , corresponding to initial current 202 in FIGS. 2A and 3A , restoring the circuit to its original state.
  • the above-described circuits can provide a single storage inductor Lstorbias, or two such storage inductors Lstorbias 1 , Lstorbias 2 in series, rather than two separate storage inductors connected to a low-voltage rail (e.g., ground), to perform the same function more efficiently.
  • the improved efficiency of the described AND/OR logic gates can result in denser circuits.
  • the above-described circuits further avoid the need for transformer couplings between storage inductors, permitting the circuit to have a simplified layout that is scalable to smaller process nodes.
  • the described circuit designs can also use a full ⁇ 0 flux bias current, which is easier to introduce than a fraction of a ⁇ 0 where a Josephson junction is used to quantize the flux bias, given that a full ⁇ 0 of current is the natural output of a Josephson junction.
  • the above examples are also capable of storing at least one ⁇ 0 of current in any of the storage inductors in the storage loops, and in some cases can store 2 ⁇ 0 .
  • FIG. 4 illustrates an example method 400 of determining logical AND and OR values based on SFQ pulse inputs.
  • An initializing current is established 402 in a bias storage loop comprising first and second logical decision JJs in an RQL AND/OR gate.
  • Positive SFQ pulses are provided 404 to assert one or both logical inputs of the RQL AND/OR gate to place 406 currents in logical input storage loops.
  • the RQL AND/OR gate can be, for example, like gates 100 or 200 shown in FIGS. 1 and 2A , such as the circuits shown in FIG. 2B or 2C , or can be extensions of such examples.
  • the RQL AND/OR gate used in the method may comprise no more than six JJs and no more than fourteen inductors, as shown in FIG. 2B .
  • One or both logical decision JJs then trigger 408 .
  • a first logical decision JJ can trigger based on both the logical inputs being asserted, and/or a second logical decision JJ can trigger based on one or both the logical inputs being asserted.
  • the second logical decision JJ may trigger further based on the presence of the current established 402 in the bias storage loop.
  • the first logical decision JJ may trigger further based on the absence of the current established 402 in the bias storage loop.
  • the first and second logical decision JJs can be configured to so trigger, for example, by making them common to multiple of the logical input storage loops, by providing appropriate biasing, and/or by appropriate component sizing.
  • a logical OR assertion signal generated as a result of the second logical decision JJ triggering, can then propagate 410 from an OR output of the RQL AND/OR gate based on one or both logical inputs being asserted.
  • a logical AND assertion signal generated as a result of the first logical decision JJ triggering, can then propagate 410 from an OR output of the RQL AND/OR gate based on both logical inputs being asserted.
  • Each of these assertion signals can be, for example, a single SFQ pulse.

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US15/811,000 US10158363B1 (en) 2017-11-13 2017-11-13 Josephson and/or gate
KR1020207012934A KR102291321B1 (ko) 2017-11-13 2018-10-17 조셉슨 and/or 게이트
PCT/US2018/056316 WO2019094162A1 (fr) 2017-11-13 2018-10-17 Josephson et/ou porte
JP2020517893A JP6894048B2 (ja) 2017-11-13 2018-10-17 ジョセフソンａｎｄ／ｏｒゲート
CA3077219A CA3077219C (fr) 2017-11-13 2018-10-17 Josephson et/ou porte
EP18799635.0A EP3711165B1 (fr) 2017-11-13 2018-10-17 Et/ou porte supraconductrice et procédé pour la détermination des valeurs et/ou à partir des pulses quantiques à flux unique
AU2018364957A AU2018364957B2 (en) 2017-11-13 2018-10-17 Josephson AND/OR gate

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